Systemic risk and the solvency-liquidity nexus of banks

Diane Pierret1,2

This version: March 28, 2014

Abstract: This paper shows the empirical interaction between solvency and liquidityrisks of banks that make them particularly vulnerable to an aggregate crisis. I find thatbanks lose their access to short-term funding when markets expect they will be insolvent ina crisis. Conversely, a bank with more short-term debt (with a large exposure to fundingliquidity risk) gets a larger capital shortfall estimate. Importantly, the short-term debt ofa bank is not sensitive to the risk of the bank failing in isolation but is influenced by itssolvency risk when the whole economy is under stress (measured as the expected capitalshortfall in a crisis). This solvency-liquidity nexus is found to be strong under many robust-ness checks and to contain useful information for forecasting the short-term balance sheet ofbanks. The results suggest that the solvency-liquidity interaction should be accounted forwhen designing liquidity and capital requirements, in contrast to Basel III regulation wheresolvency and liquidity risks are treated separately.

Keywords: capital shortfall, funding liquidity risk, short-term funding.

JEL Classification: G01, G21, G28.

1NYU Stern School of Business, Volatility Institute, 44 West 4th Street, New York, NY 10012.2Université catholique de Louvain, ISBA, 20 Voie du Roman Pays, B-1348 Louvain-La-Neuve, Belgium.

E-mail: dpierret@stern.nyu.edu

I am extremely grateful to Viral Acharya, Luc Bauwens, Robert Engle and Christian Hafner for theirexcellent guidance and continuous support. I thank Stephen Figlewski, Andres Liberman, Matteo Luciani,Matthew Richardson, Sascha Steffen and David Veredas for helpful comments. I also thank Rob Capellinifor providing me with V-Lab’s measures of systemic risk. All remaining errors are my own.

“A more interesting approach would be to tie liquidity and capital standards together byrequiring higher levels of capital for large firms unless their liquidity position is substantiallystronger than minimum requirements. This approach would reflect the fact that the marketperception of a given firm’s position as counterparty depends upon the combination of itsfunding position and capital levels. [...] While there is decidedly a need for solid minimumrequirements for both capital and liquidity, the relationship between the two also matters.Where a firm has little need of short-term funding to maintain its ongoing business, it isless susceptible to runs. Where, on the other hand, a firm is significantly dependent on suchfunding, it may need considerable common equity capital to convince market actors that it isindeed solvent. Similarly, the greater or lesser use of short-term funding helps define a firm’srelative contribution to the systemic risk latent in these markets.” - Remarks by Daniel K.Tarullo, Member of the Board of Governors of the Federal Reserve System, Peterson Institutefor International Economics, May 3, 2013.

1 Introduction

The main function of banks is to provide liquidity by offering funding (deposits) that ismore liquid than their asset holdings (Diamond and Dybvig (1983)). This liquidity mis-match, part of their business model, makes banks vulnerable to runs as creditors can de-mand immediate repayment when the bank faces asset shocks. The rationale for studyingthe solvency-liquidity nexus of banks is based on the literature explaining bank runs basedon the strength of the bank’s fundamentals. In Allen and Gale (1998), banking panics arerelated to the business cycle where creditors run if they anticipate that the bank’s asset val-ues will deteriorate. Similarly, Gorton (1988) shows that bank runs are systematic responsesto the perceived risk of banks.

Theoretical models on the two-way interaction between solvency and liquidity have beenmore recently developed. Diamond and Rajan (2005) show that bank runs, by making banksinsolvent, exacerbate aggregate liquidity shortages. In Rochet and Vives (2004), there is anintermediate range of the bank assets value for which the bank is still solvent but can fail iftoo many of its creditors withdraw, and the range of the interval decreases with the strengthof the bank’s fundamentals. Then, Morris and Shin (2008) explain that bank runs comefrom both the bank’s weak fundamentals and the “jitteriness” of its creditors. Therefore, thefailure region of the bank would be smaller if both the bank and its creditors held more cash.

An implication of this literature is that systemic risk is likely to play a key role in the

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solvency-liquidity nexus through the liquidation costs caused by fire sales in a crisis. If thefirm fails in isolation, its illiquid assets can be liquidated for a price close to their value inbest use (Shleifer and Vishny (1992)).1 In a systemic crisis, however, potential buyers will beunable to find funding to buy the assets of the distressed firm. Creditors will consequentlyrun from banks that are vulnerable to an aggregate shock as they anticipate these banks willnot be able to repay them in a crisis.

While the solvency-liquidity nexus has been well studied theoretically in the economicliterature, the interaction between solvency and liquidity risks tends to be omitted in thenew capital and liquidity regulatory standards. The liquidity coverage ratio (LCR) of BaselIII imposes that financial firms hold a sufficient amount of high-quality liquid assets to covertheir liquidity needs over a month of stressed liquidity scenario.2 However, the liquidityneeds according to this standard are essentially a function of the funding mix of the bankand do not depend on other bank’s fundamentals, in particular, on its capital adequacy andasset risks. Similarly, the required capitalization of a bank in Basel III is not related to itsexposure to funding liquidity risk.3

The solvency-liquidity nexus of banks has also not been the center of empirical studiesinvestigating funding liquidity risk of the financial sector.4 In this paper, I fill this gap inthe literature and test whether the solvency-liquidity nexus of banks empirically holds byexamining the short-term balance sheet of 50 US bank holding companies over 2000-2013.

1Other fire-sale papers also relying on the Shleifer and Vishny (1992) insight include Allen and Gale(1998, 2000a,b, 2004); Acharya and Yorulmazer (2008); Acharya and Viswanathan (2011); Diamond andRajan (2005, 2011).

2Next to the LCR, Basel III also introduces a Net Stable Funding Ratio (NSFR). The NSFR is the ratioof available stable funding to required stable funding over a one year horizon. The required stable funding isdetermined based the institution’s assets and activities (Basel Committee on Banking Supervision (2011)).

3Funding liquidity risk is only likely to play a modest role via the interconnectedness measure usedto derive the additional capital requirement for globally systemically important financial institutions (G-SIFIs). The systemic importance measure is the equally-weighted average of the size, interconnectedness,lack of substitutes for the institution’s services, global activity and complexity (Basel Committee on BankingSupervision (2013b)). Interconnectedness is itself based on three indicator measures: intra-financial systemassets, intra-financial system liabilities, and securities outstanding.Alternatively, some supervisory stress test models explicitly feature funding liquidity feedbacks from the

deterioration of the banks’ fundamentals as in the risk assessment model for systemic institutions (RAMSI)of Aikman et al. (2009) used at the Bank of England.

4Related empirical studies include Das and Sy (2012) who document the trade-off between solvency andliquidity; banks with more stable funding and more liquid assets do not need as much capital to get thesame stock return. Gorton and Metrick (2012) find that increases in repo rates are correlated to higheraggregate counterparty risk, whereas increases in repo haircuts are correlated to higher uncertainty aboutcollateral values. Afonso et al. (2011) study the Fed funds market and find increased sensitivity to bank-specific counterparty risk during times of crisis (both in the amounts lent to borrowers and in the cost ofovernight funds).

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Short-term debt mainly consists of Fed funds purchased and repurchase agreements (repos),uninsured deposits and other short-term borrowings. Short-term assets include cash, Fedfunds sold and reverse repos, and short-term debt securities.

The difference between short-term debt and short-term assets is used in this paper asa proxy for the exposure of a firm to funding liquidity risk. When liquidity conditions aretight, a financial firm faces the risk of not being able to roll-over its existing short-term debtand/or to raise new short-term debt. To survive a crisis, a firm needs a sufficient amountof liquid assets that can be converted into cash when the bank’s short-term funding startsdrying up. The gap between its short-term debt and short-term assets — the liquid assetshortfall — represents the amount of liquid assets that would be left if the bank lost itscomplete access to short-term funding (see Figure 1).

I test for the solvency-liquidity nexus using a fixed-effects panel vector autoregressive(VAR) model. In particular, I test for the interaction between solvency and liquidity usingseveral measures of solvency risk: regulatory capital ratios, market measures of risk (realizedvolatility, expected shortfall and market beta), and a measure of the expected capital short-fall (SRISK) of the bank under aggregate stress defined by Acharya et al. (2010, 2012);Brownlees and Engle (2011). According to SRISK, a firm is adequately capitalized to sur-vive a crisis if its ratio of market capitalization to total assets remains larger than 8% whenthe market index falls by 40% over the next six months. This measure is an alternative tothe capital shortfall estimates of stress tests that is purely based on publicly available marketdata (and therefore available at a higher frequency than stress tests outcomes).

I document four important results. First, I find that the bank’s capital shortfall understress (SRISK) determines how much short-term debt it can raise. This result supportsthe models of Allen and Gale (1998); Diamond and Rajan (2005), etc. explaining bank runsbased on the strength of the bank’s fundamentals. Conversely, the expected capital shortfallof a bank increases when the bank holds more short-term debt (has a larger exposure tofunding liquidity risk), in line with the introductory quote of D. Tarullo and some previousevidence that firms with more maturity mismatch have a larger contribution to systemic risk(Adrian and Brunnermeier (2010)). Figure 2 illustrates well the solvency-liquidity nexuswhere capital-constrained banks (i.e. banks with a positive SRISK) had a larger averageexposure to liquidity risk (measured by the difference between short-term debt and short-term assets) than adequately capitalized banks until 2011. The average liquidity shortfall ofcapital-constrained banks reached a maximum of $133 billion in the third quarter of 2007.This exposure made them particularly vulnerable to the sudden freeze of short-term funding

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markets that followed.Second, I show that not all solvency risk measures predict the short-term debt level of

banks. The expected capital shortfall SRISK interacts well with the level of short-termfunding of the bank compared to other measures of solvency risk because (i) it is a measureof the bank’s exposure to aggregate risk, and (ii) it combines both book and market values.Relating to the model of liquidation costs of Shleifer and Vishny (1992), this result suggeststhat a bank with higher solvency risk in isolation does not necessarily get restricted accessto short-term funding. What matters most for the suppliers of short-term funding is thevulnerability of the bank to an aggregate crisis. When this crisis occurs, ’pure’ solvency risk(measured by the Tier 1 leverage ratio), amplified by market shocks, explains the bank’saccess to short-term funding.

Third, the stressed solvency risk measure interacts with the bank’s profitability (measuredby its net income divided by total assets) in determining its short-term balance sheet. Whilea more profitable bank has a larger access to short-term funding and does not hold as muchliquid assets, profitability does not have this beneficial effect on its short-term balance sheetwhen the bank is expected to be capital-constrained in a crisis. For example, the positivenet income of $2 billion of Citigroup in the third quarter of 2007 did not prevent the bankfrom losing 18% of its short-term funding (-$172 billion) the next quarter, as Citigroup wasalso highly undercapitalized according to SRISK ($51 billion expected capital shortfall in2007Q3).

Finally, out-of-sample forecasting results during the European sovereign debt crisis showthat the solvency-liquidity interaction helps improve the forecasts of the short-term balancesheet of banks. Omitting SRISK in the model increases the forecasting errors of the liquidasset shortfall considerably and particularly for capital-constrained banks.

Overall, the results of this paper suggest that the solvency-liquidity nexus should beaccounted for when designing liquidity and capital requirements, in contrast to Basel III reg-ulation where liquidity and solvency risks are treated separately. The paper gives empiricalsupport to the approach advanced by Tarullo (2013) to tie liquidity and capital requirementstogether by requiring banks with a large exposure to short-term funding to hold an addi-tional capital buffer. The liquid asset buffer of the LCR might be a sufficient requirementfrom a microprudential perspective. However, the sudden drop in short-term funding fora bank that has a perfectly maturity-matched securities book (including repos and reverserepos) may also result in fire sales and increases the risk of contagion by transferring fundingliquidity risk to the bank’s customers. The supplementary capital buffer is a preemptive

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measure that would give the confidence to creditors to continue to provide funding to thebank in a period of aggregate stress.

The rest of the paper is structured as follows. In Section 2, I describe the short-termbalance sheet of banks and their solvency risk measures. I test the solvency-liquidity nexusin Section 3. I comment on the out-of-sample forecasting results in Section 4.

2 Short-term balance sheet and solvency risk measures

2.1 Long-term vs. short-term balance sheet and the liquid assetshortfall

The sample considered in this paper is a panel of 49 publicly traded US bank holdingcompanies (BHC) reporting their regulatory accounting data over 13 years from 2000Q1 until2013Q1 (i.e. 53 quarters). This sample of banks corresponds to the intersection betweenthe NYU Volatility Laboratory (V-Lab) sample for its global systemic risk analysis (thatwill be introduced in the next section) and the bank holding companies reporting under theFR Y-9C schedule (equivalent to the Call Reports of Condition and Income of commercialbanks). The names of the BHCs and their market capitalizations are reported in AppendixD.

I construct the short-term debt and short-term asset variables of these BHCs based onitems extracted from their FR Y-9C reports from the SNL Financial database. The short-term debt is constituted of uninsured time deposits of remaining maturity of less than a year,securities sold under agreements to repurchase (repos), Federal funds purchased, and otherborrowed money of remaining maturity of less than a year. The short-term assets includedebt securities of remaining maturity of less than a year, interest-bearing bank balances(cash), securities purchased under agreements to resell (reverse repos), and Federal fundssold. The components of short-term debt and short-term assets are described and illustratedin Appendix A.

As the panel data set is unbalanced, I will restrict the following analyses to a smallersample of 44 banks for which the time series dimension is larger than 30 observations.5 Itest the stationarity of the balance sheet quantities (in logarithms) in Appendix B usingthe panel unit root test robust to cross-sectional dependence of Pesaran (2007). This testindicates that the permanent impact of a shock on the size of a bank comes from shocks in

5This restriction excludes Goldman Sachs and Morgan Stanley from the sample as they obtained thestatus of bank holding company at the end of 2008.

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the long-term balance sheet (where the unit root hypothesis is not rejected), whereas theshort-term balance sheet shocks revert to a trend level.6 This result is consistent with thelong-term balance sheet being the core business of the traditional bank that invests insureddeposits (part of the long-term debt) in loans (long-term assets).7

The evolution of the average balance sheet of banks is shown in Figure 3. The averagesize of the balance sheet (measured by total assets) triples (from $85 billion to $280 billion)over the sample period and follows an increasing trend in the long-term balance sheet. Overthis period, and particularly during the financial crisis, salient events include the acquisitionof out-of-sample banks by in-sample banks; Golden West Financial sold to Wachovia in May2006, Bear Stearns sold to J.P.Morgan in March 2008, Countrywide to Bank of Americain July 2008, Washington Mutual to J.P.Morgan and Merrill Lynch to Bank of America inSeptember 2008, and the acquisition of in-sample banks by other in-sample banks; NationalCity Corp. sold to PNC and Wachovia to Wells Fargo in the last quarter of 2008.

For the purpose of testing the solvency-liquidity nexus, this paper focuses on the short-term part of the balance sheet. The acquisition of two major investment banks (Bear Stearnsand Merrill Lynch) in 2008 brought a considerable amount of short-term debt and short-term assets in the banking sector (mostly in the form of repos and reverse repos). Theincrease in the average short-term balance sheet is considerable with the purchase of BearStearns (visible on J.P.Morgan’s balance sheet in 2008Q3). In comparison, the impact of theacquisition of Merrill Lynch (visible on Bank of America’s balance sheet in 2009Q1) on theaverage short-term balance sheet is attenuated as several large banks were losing a significantamount of short-term funding at that time.

In contrast to an overall increasing trend in short-term assets, the average short-termdebt slowed down in 2007Q3 with the first signs of a “run on repo” in August 2007 (Gortonand Metrick (2012)), visible on the short-term balance sheet of several large banks includingCitigroup that lost $172 billion (18%) of short-term debt from 2007Q3 to 2007Q4. Theaverage short-term debt reached a peak in the third quarter of 2008 (with the acquisition ofBear Stearns) and declined afterwards.

The gap between the short-term debt and short-term assets of a bank — its liquid assetshortfall — represents the amount of liquid assets that would be left if the bank lost itscomplete access to short-term funding.8 The average liquidity gap of the banking sector (also

6The trend stationarity of the short-term balance sheet allows estimating a dynamic panel data modeldirectly on the levels in Section 3 by applying standard estimation and inference techniques.

7The long-term debt (resp. assets) is the difference between total liabilities (resp. assets) and short-termdebt (resp. assets).

8Also note that short-term assets will serve in this paper as a proxy for liquid assets due to the lack of

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shown in Figure 3) was the widest at the end of 2007 making banks particularly vulnerable tothe sudden freeze in short-term funding markets. The short-term funding freeze was furtheraccentuated with credit risk concerns at the end of 2008 with Lehman Brothers’ bankruptcyand the most negative average net income of banks over the sample period ($-850 million).

Since the financial crisis, the average liquid asset shortfall of banks has been decliningto become negative in 2011 (i.e., banks now hold more short-term assets than short-termdebt). Several circumstances explain the increase of banks’ stock of short-term assets. Afirst explanation is linked to the persistent effect of the financial crisis on the real economywhere the demand for loans has been slowly recovering and outpaced by deposit growth. Asa result, banks have been investing in securities and (profitable) treasury products.9 In orderto obtain secured short-term funding, banks also need to hold more short-term liquid assetsthan before due to stricter collateral requirements (higher haircuts). Then, higher liquidasset holdings by banks respond to precautionary concerns by banks (protecting againstanticipated interest rate increase) and the regulator. Banks are encouraged by regulationto hold more short-term liquid assets to comply with both liquidity requirements (BaselIII liquidity coverage ratio) and capital requirements (as holding short-term assets usuallyinvolves low regulatory capital requirements).

2.2 Solvency risk measures

2.2.1 Regulatory capital ratios

The regulator usually employs capital ratios to assess the solvency risk of a bank. Figure 4displays the average regulatory capital ratios: the Tier 1 common capital ratio (T1CR) andthe Tier 1 leverage ratio (T1LV GR). The Tier 1 common capital ratio is the ratio of Tier 1common equity to risk-weighted assets, whereas the Tier 1 leverage ratio is the ratio of Tier1 capital to total assets. The upward shift in regulatory capital ratios in the fourth quarterof 2008 indicates a healthier banking system and coincides with the launch on October14, 2008 of the Capital Purchase Program (CPP) and the Temporary Liquidity GuaranteeProgram (TLGP) under the Trouble Asset Relief Program (TARP). By purchasing assets

historical data for the assets included in the high-quality liquid assets (HQLA) definition of Basel III. Highquality liquid assets include cash, reserves at central banks, treasury bonds, and non-financial corporatebonds and covered bonds with the highest ratings. Additional assets like highly-rated RMBS, non-financialcorporate bonds and covered bonds with [A+, BBB-] rating, and common equity shares can be included inthe HQLA stock with the appropriate haircuts specified in the LCR revision of 2013 (Basel Committee onBanking Supervision (2013a)).

9“US banks brace for interest rate rises”, Financial Times, February 24, 2011. “Excess deposits demandnovel responses”, Financial Times, May 30, 2012.

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and equity from troubled banks from October 2008 on, the TARP led to a significant increasein the average capital ratios. For example, Treasury bought $25 billion of preferred sharesof Citigroup in October 2008 and another $20 billion in November 2008 under the CPP.10

2.2.2 Expected capital shortfalls in a crisis

Acharya et al. (2012) define the systemic risk contribution of a firm i to the real economyat time t as “the real social costs of a crisis per dollar of capital shortage(t)× Probabilityof a crisis(t) × SRISKit”, where SRISKit represents the expected capital shortfall of thefirm in a crisis, i.e. when the market equity index drops by 40% over the next six months.In these market conditions, SRISK is based on the assumption that the book value of the(long-term) debt Dit of the bank will remain constant over the six-month horizon whileits market capitalization MVit will decrease by its six-month return in a crisis, called thelong-run marginal expected shortfall (LRMES). The expected capital shortfall in a crisisSRISK of bank i at time t is defined by

SRISKit = Et[k(Dit+h +MVit+h)−MVit+h|Rmt+h ≤ −40%] (1)

= kDit − (1− k) ∗MVit ∗ (1− LRMESit)

where Rmt+h is the return of the market index from period t to period t + h (h = 6months), k is the prudential capital ratio (8% for US financial firms), and LRMESit =

−Et(Rit+h|Rmt+h ≤ −40%). Compared to other market-based measures of systemic risk likethe CoVaR of Adrian and Brunnermeier (2010) or the Distress Insurance Premium (DIP)of Huang et al. (2012), an interesting feature of SRISK is that it is a function of size andleverage which are two characteristics that the regulator finds particularly relevant whenmeasuring solvency risk of banks. SRISK can be written as a function of size, leverage andrisk

SRISKit = MVit {k(Lvgit − 1)− (1− k)(1− LRMESit)} (2)

where Lvgit is the quasi-market leverage defined as the ratio of quasi-market assets to marketcapitalization (Lvgit = (MVit + Dit)/MVit). Therefore, the capital shortfall of a bank willbe large if the bank is large, highly leveraged and highly sensitive to an aggregate shock asmeasured by LRMESit.

These measures (SRISK and LRMES) are available from the V-Lab website developedat NYU Stern School of Business.11 In the global systemic risk analysis of V-Lab, LRMES

10See http://www.treasury.gov/initiatives/financial-stability/reports/Pages/TARP-Tracker.aspx.11See http://vlab.stern.nyu.edu/.

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is extrapolated from its short-term counterpart MES representing the daily return of thebank conditional on a 2% decline in the daily return of a global market index. The MESis derived from a time-varying beta estimated with the Dynamic Conditional Beta model ofEngle (2012) that accounts for asynchronous trading around the world when measuring thecomovement of bank returns with a global market index.

By definition, SRISK can be negative when a bank is expected to hold a capital excess ina crisis. In Figure 4, we find two different regimes for the average SRISK of banks. SRISKwas indeed negative for most banks before 2007. The average SRISK was the lowest in thethird quarter of 2006 then started to increase in 2007. SRISK became positive in the fourthquarter of 2007 and reached a maximum average capital shortfall of $16 billion in the firstquarter of 2009. The average capital shortfall has remained positive since the financial crisisand bumped several times afterwards, in particular in the heat of the European sovereigndebt crisis in 2011.

3 Testing the solvency-liquidity nexus of banks

As liquidity risk concerns both sides of the balance sheet, I test the interaction betweensolvency risk and both the short-term debt and short-term assets. Panel unit root testsindicate that the variables yit = ln(STDebtit), zit = ln(STAssetsit), and the solvency riskmeasure SRISKit/TAit are trend stationary (see Appendix B). Therefore, the solvency-liquidity nexus is tested using a fixed-effects panel vector autoregressive (VAR) model forthe (K × 1) vector of endogenous variables wit

wit = αi + Φwit−1 + θt+ εit, t = 1, 2, ..., Ti, i = 1, 2, ..., N, (3)

where αi are bank dummies, θ is a trend parameter and Φ is a (K × K) matrix of VARparameters.12 Based on in-sample fit criteria, I augment the panel VAR process of eq. (3)to allow for heterogenous trend and heterogenous dynamic parameters

wit = αi + φi � wit−1 + θit+ δwit−1 + εit, (4)

where φi, θi are (K × 1) vectors of parameters specific to bank i, δ is a (K ×K) matrix ofparameters with zeros on the diagonal, and � is the Hadamard product.

12The parameters of eq. (3) are estimated by ordinary least squares. The bias of OLS parameter estimatesis likely to be small for the considered sample since the minimum size of the time series dimension for eachbank is 30 observations (i.e. Ti ≥ 30, ∀i).

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The estimates of the interaction parameters (δ) of equation (4) are reported in Table1 where wit = (yit, zit, SRISKit/TAit)

′. This Table reveals the empirical solvency-liquiditynexus where banks with a larger expected capital shortfall find it more difficult to raiseshort-term funding; the estimates suggest that a positive unit shock on the ratio of SRISKto total assets produces a -1.102% shock on the short-term funding of the bank. On theother leg of the interaction, a 1% increase in the short-term debt of the bank increases itscapital shortfall ratio by 0.009. Therefore, the interaction between solvency and short-termdebt is asymmetric; higher solvency risk limits the access of the firm to short-term fundingbut a firm with more short-term debt has a higher risk of insolvency in a crisis.

This result supports the theoretical literature explaining bank runs based on the strengthof the banks fundamentals (Allen and Gale (1998); Diamond and Rajan (2005), etc.), anddescribing the interaction between liquidity and solvency problems of banks (Diamond andRajan (2005); Morris and Shin (2008); Rochet and Vives (2004)). The results also giveempirical support to the recent speeches by Carney (2013) and Tarullo (2013) explainingthat the repair of banks’ balance sheet (i.e. higher capital levels) gives the confidence toinvestors and creditors to continue to provide funding to banks.

From Table 1, we also note that short-term assets do not relate to the other variablesin the vector wit, suggesting that banks are not able to adjust their stock of short-termassets to solvency risk or short-term funding conditions in a timely fashion. It also reflectsa liquidity hoarding tendency of banks where banks prefer to sell long-term assets to repayshort-term creditors. Banks prefer to hold the short-term assets for precautionary reasonsor for investing in fire sale assets of other financial institutions that are expected to generatehigh future returns (Acharya et al. (2009)).

In the rest of this section, I test alternative solvency risk measures to predict the short-term balance sheet of banks in Section 3.1, for the interaction between profitability andsolvency risk in predicting the short-term balance sheet (Section 3.2), and for the robustnessof the solvency-liquidity nexus in Section 3.3.

3.1 Testing alternative solvency risk measures

I report the tests of alternative measures of solvency risk to predict the short-term balancesheet (yit and zit) in Table 2, controlling for the market-to-book ratio as the regressionincludes both accounting and market variables. The columns (1) to (6) show the individualimpact of each measure. From this Table, the regulatory capital ratios (T1CR and T1LV GR)do not appear to be related to either side of the short-term balance sheet. Market measures

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of risk like the realized quarterly volatility is significant (at 5%) to predict short-term assetsbut this result does not hold in the regression including all solvency risk factors (column (7)).Then, the sensitivity of the bank’s return to market shocks measured by the the DynamicConditional Beta (DCB) of Engle (2012), and the contribution of the bank to systemic riskmeasured by the Delta CoVaR of Adrian and Brunnermeier (2010) are not significant driversof the short-term balance sheet either. When all solvency risk factors are included in theregression (column (7)), only SRISK per unit of asset and the market-to-book ratio aresignificant at the 1% level to predict the short-term debt level of banks.

The results of Table 2 suggest that not all solvency risk factors can predict the shocks inthe short-term balance sheet of banks. A bank with higher solvency risk in isolation doesnot necessarily get restricted access to short-term funding. However, banks lose short-termfunding when they are expected to be insolvent in a systemic crisis. An explanation for thisobservation is based on the liquidation costs of a firm’s illiquid assets in a crisis. Shleifer andVishny (1992) show that when a firm is individually in distress, its liquidation costs are notas high because the firm can find buyers in the same industry who value its illiquid assetsat a price close to their value in best use. In a crisis, however, the potential buyers in theindustry will likely also meet difficulties to find funding and will not be able to buy thoseassets. The firm will then have to sell its illiquid assets to less specialized buyers outside theindustry at a higher liquidation cost.

A bank that is expected to be insolvent in a crisis will be facing high liquidation costs andwill consequently not be able to raise cash. Creditors who anticipate this based on publiclyavailable data (as those used to derive SRISK) will run from the bank as they expect thebank will not be able to repay them. The liquidation costs during the 2008 financial crisiswere exacerbated by the huge gap between short-term assets and short-term debt observedin Section 2. As a result, banks had no choice but to sell illiquid assets to repay creditorswhen losing access to short-term funding.

In-sample fit criteria show the superiority of SRISK in Table 3 (first column) to predictshort-term funding; the adjusted R2 is 15.7% compared to an adjusted R2 around 11% forthe regressions with the alternative solvency risk measures of Table 2.13 In order to identifywhat works so well in SRISK for predicting the short-term funding of banks, Table 3 alsoreports the estimates of the different components of SRISK highlighted in eq. (2). TheTable shows that the improvement in in-sample fit rather comes from the ratio of market

13Note that all reported R2 are on the first differences (wit −wit−1). The R2 of levels (wit) are very high(around 90%) given the bank specific constant, trend and autoregressive parameters.

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capitalization to total assets (MV/TA) than from the long-run marginal expected shortfall(LRMES) or the quasi-market leverage (Lvg). The main difference between Lvg and theMV/TA ratio is a different combination of book and market values; the ratioMV/TA is theproduct of the book leverage ratio (T1LV GRit) and the market-to-book ratio (MVit/BVit)

MVit

TAit

=BVit ∗

(MVit

BVit

)TAit

' T1LV GRit ∗(MVit

BVit

),

whereas Lvgit = 1 + Dit

MVitis not a function of the book leverage ratio. A potential argument

against using market values to test for the solvency-liquidity nexus is that market valuesalso incorporate information about liquidity risk. The results of Table 3 however suggestthat both the book solvency ratio — informing about pure solvency shocks — and themarket-to-book ratio — informing about how faster the market values fall compared to bookvalues — are important for predicting the short-term debt of banks. The ratio MV/TA ishighly correlated to the book leverage ratio (0.91) and less correlated to the market-to-bookratio (0.44); solvency risk amplified by market shocks explain banks’ access to short-termfunding and neither the market-to-book or the leverage ratio taken separately, nor theirlinear combination predict short-term funding.

The modest improvement in fit due to the downside risk of the bank LRMES (0.66%increase of adjusted R2 from column 4 to column 5, Table 3) is consistent with the sampleperiod that contains several episodes of market stress. In a crisis, all is already functionof the aggregate shock. However, measuring the downside risk is important preemptively;I find increasing out-of-sample forecasting errors when MV/TA is employed in the panelVAR instead of SRISK/TA for predicting the short-term balance sheet of banks during theEuropean sovereign debt crisis (especially with the dynamic forecasting exercise of Section4).

3.2 Interaction between solvency and profitability

In Perotti and Suarez (2011), both liquidity risk and profitability are increasing functionsof the short-term debt level of the bank. A bank will indeed demand more short-termfunding when it finds profitable investment opportunities. Its liquidity risk will also increaseas its short-term debt will be invested in long-term profitable assets. The impact of theprofitability of the bank measured by its net income divided by total assets is found to bepositive on short-term debt and negative on short-term assets in Table 4 (Panel A), butthese parameters are not significant at the 5% level.

12

The parameters of eq. (4) are however expected to vary with the state of the bank and/orthe aggregate liquidity conditions. In good times, short-term funding and short-term assetsare the result of management decisions and are driven by demand factors. As mentioned,banks with profitable opportunities will demand more short-term funding. In bad times,supply factors determine how much short-term debt a bank can raise and the short-termassets adjust accordingly. One way to disentangle supply and demand effects on the bankcharacteristics is to augment equation (4) with a state variable

wit = αi + φi � wit−1 + θit+ δwit−1 + γwit−1 ∗ st−1 + ωst−1 + εit (5)

where ω is a (K×1) vector of parameters, γ is a (K×K) matrix of parameters with zeros onthe diagonal, and the state variable st could be a bank characteristic or a common factor. Forexample, Cornett et al. (2011) use the TED spread (the difference between 3-month LIBORrate and T-bill rate) to reflect the change in the management of liquidity risk exposuresof banks during the financial crisis.14 In Table 4 (Panel B), I show that a good candidatefor the state variable is simply a dummy variable equal to one when SRISK is positive(sit = 1{SRISKit>0}), i.e. when the bank is expected to have a capital shortfall in a crisis.

This distinction between states where SRISK is positive or negative appears to beimportant when measuring the effect of the profitability of the bank on its short-term balancesheet. Indeed, a bank with a higher net income has a larger access to short-term fundingwhile it does not hold as much liquid assets. In Table 4, this beneficial effect of the bank’sprofitability on its short-term balance sheet appears to be true only when the bank’ SRISKis negative, i.e. when the bank is adequately capitalized to survive a crisis (sit = 0). Whenthe bank is expected to be capital-constrained in a crisis (sit = 1), the effect of profitabilityon its balance sheet disappears (δ + γ ' 0), and only supply factors predict the short-termdebt of the bank.

An interesting observation is that the contrasting impact of profitability on the short-termbalance sheet can be reproduced when I allow for parameter breaks over time

wit = αi + φi � wit−1 + θit+ δwit−1 + δcwit−1 ∗ ct + δpcwit−1 ∗ pct + ωcct + ωpcpct + εit (6)

where ct and pct are dummy variables indicating whether the quarter t belongs to the financialcrisis period (2007Q1-2009Q4) or the post crisis period (2010Q1-2013Q1) respectively. InTable 11 (Appendix C), we observe that the impact of the net income on the short-term

14The TED spread is however not significant to predict the short-term balance sheet for the sampleconsidered in this paper (cf.. Section 3.3.2).

13

balance sheet also disappeared during the financial crisis (δ + δc ' 0). This Table furthershows that SRISK was significant only during the financial crisis (when there was actualliquidity stress). The results tend to confirm the interpretation of SRISK as a supply factorfor short-term funding, and of the net income as a demand factor when the firm is adequatelycapitalized.

Based on the estimates of the panel VAR, I can derive the impulse response functions(IRF) of wit where wit = (yit, zit, NetIncomeit/TAit, SRISKit/TAit)

′. I collect the orthogo-nalized shocks of the VAR from a Cholesky decomposition of the covariance matrix of εit ofeq. (4), with the ordering given by [NetIncomeit/TAit → SRISKit/TAit → yit → zit]. Thisordering is motivated by the observation that exogenous shocks first impact a firm via itsactivities and is translated into the net income, markets react by adjusting their assessmentof the capital shortfall SRISK, this in turn affects how much funding the bank can accessand the short-term assets adjust in consequence.

Due to the heterogenous autoregressive parameters of eq. (4), firms will have heteroge-neous responses to sigma shocks. In Figure 5, I show the median impulse response functionto orthogonalized sigma shocks between the 25% and the 75% IRF quantiles to assess theheterogeneity in impulse responses across firms. In general, the IRF that concerns short-termfunding are more heterogenous (impact of other variables shocks on short-term debt and im-pact of short-term debt shocks on other variables). The range between impulse responsesquantiles is also wider for the interaction between SRISK and the short-term balance sheet.For some banks, it takes three years for the impact of SRISK shocks on short-term fundingto vanish whereas the solvency shocks of other banks have a more definitive impact on theirshort-term funding. Then, the impulse response functions well illustrate previous findingson the asymmetric impact of shocks between SRISK and the short-term balance sheet, andbetween the net income and the short-term debt.

The impact of orthogonalized sigma shocks will be different when I differentiate betweencapital-constrained vs. adequately capitalized banks based on the parameters of eq. (5).Figure 6 shows the gap in median impulse response functions between adequately capitalizedversus capital-constrained firms. The solvency-liquidity nexus appears to be exacerbatedfor capital-constrained banks; the impact of solvency shocks on short-term funding doublescompared to adequately capitalized banks, while the response of short-term debt to shocks inother bank characteristics (net income and short-term assets) is less important and vanishesmore rapidly. For capital-constrained banks, only the solvency-liquidity nexus appears toexplain the short-term balance sheet.

14

3.3 Robustness of the solvency-liquidity nexus

3.3.1 Robustness to TARP

On October 14, 2008, the U.S. government announced a series of measures — the TroubledAsset Relief Program (TARP) — to restore financial stability. Under the TARP, the Trea-sury Department launched the Capital Purchase Program (CPP) and the Federal DepositInsurance Corporation launched the Temporary Liquidity Guarantee Program (TLGP). Un-der the CPP, Treasury injected $205 billion capital into banks by buying warrants, commonshares, and preferred shares.15 Under the TLGP, the FDIC allowed financial institutions toretain and raise funding by giving a guarantee on existing noninterest-bearing transactionaccounts and certain newly issued senior unsecured debt. Data on the amount and maturityof total unsecured debt issued by banks and guaranteed by the FDIC are publicly available.16

It is possible to derive the amount of short-term debt a bank would have had if it did nothave access to TLGP funding. The solvency-liquidity nexus estimates hardly change whenTLGP funding is not taken into account. It is however impossible to project this scenarioon the other variables of the panel VAR as it requires to know where TLGP funding wasinvested and how markets would have reacted in this scenario.

If we assume that banks received help from the TARP when they actually needed it,the amount of CCP capital injected and the amount of TLGP funding received are realizedmeasures of the bank’s capital shortfall and liquidity shortfall, respectively. The largestbanks received the largest injections of capital and liquidity. Looking at data from the secondquarter of 2008, I test different bank characteristics and risk measures to explain their capitaland liquidity shortfalls divided by their total assets. In Table 5, I report the estimates ofcross-sectional regressions for a sample of 17 banks that received both capital and liquidityinterventions. It appears that the regulatory capital ratios are the most important factorsexplaining government interventions. After controlling for the size, we observe that banksthat received help from the CPP and banks that received help from the TLGP have differentprofiles. Banks that received government secured debt had low Tier 1 leverage ratios (ratioof Tier 1 capital to total assets), whereas banks that received capital injections had low Tier1 Common capital ratios (ratio of Tier 1 Common capital to risk-weighted assets). Bankswith high liquidity shortfalls in 2008Q4 had a large short-term balance sheet, high cost offunding, and high market beta (or LRMES) in 2008Q2. Conversely, banks with high capital

15http://www.treasury.gov/initiatives/financial-stability/TARP-Programs/bank-investment-programs/cap/Pages/overview.aspx

16See http://www.fdic.gov/regulations/resources/TLGP/index.html

15

shortfalls were more traditional banks with a large long-term balance sheet (deposits andloans), high yields on earning assets, and low market beta (among the banks that receivedgovernment interventions).

3.3.2 Common factors

The short-term balance sheets of firms are expected to co-move according to the aggregateliquidity conditions. To capture these common effects, I consider the macroeconomic andfinancial factors that are used in Fontaine and Garcia (2012) to relate to their factor mea-suring the value of funding liquidity, and will test the robustness of the solvency-liquiditynexus to these factors in the next section. The sensitivity of the short-term balance sheet(and its covariates) to the common factors is tested in

wit = αi + φi � wit−1 + θit+ β′ft−1 + εit (7)

where wit = (yit, zit, NetIncomeit/TAit, SRISKit/TAit)′, and ft is a vector of common fac-

tors. Note that common factors do not necessarily need to be lagged but this allows for thederivation of one-step ahead forecasts for wit without specifying a model for the commonfactors. The estimated parameters of common factors of eq. (7) are reported in Table 6.17

Interest rates are expected to play an important role on the short-term balance sheet.Three factors related to interest rates are considered; the level of interest rates is capturedby the Fed funds rate, the difference between long-term and short-term rates is measuredby the slope factor of the Treasury yield curve, and the TED spread reflects the perceivedcounterparty risk of interbank loans compared to Treasury loans. The TED spread is usuallyreferred as an aggregate funding liquidity risk factor (Cornett et al. (2011); Fontaine andGarcia (2012)). In the sample considered, the TED spread is not significant to explain theshort-term balance sheet directly but has a negative impact on the profitability of banks anda positive impact on their solvency risk (measured by SRISK).

The Treasury slope factor measures the difference between long-term and short-terminterest rates. A steeper term structure indicates higher profitability of investing short-termfunding in long-term assets (Fontaine and Garcia (2012)). This factor also reflects businesscycles and could be interpreted as a demand factor for liquidity. It is therefore not surprisingthat short-term debt increases with a steeper slope of the Treasury yield curve.

17Data sources of common factors: Federal Reserve Board Selected Interest Rates - H.15 (Fed fund rate);FRB Money Stock Measures - H.6 (M2 money supply growth); FRB Financial Accounts of the United States- Z.1 (MMMF flows, mortgage growth); Department of the Treasury (Treasury yield curves); Bloomberg(VIX).

16

The positive and significant coefficient of the Fed funds rate on short-term debt is moresurprising and possibly reflects an endogenous response of the Federal Reserve to fundingconditions during the financial crisis. The impact of interest rates on bank’s funding mayhowever be subtler. Diamond and Rajan (2005) explain that higher interest rates do notalways lead to lower excess demand for liquidity because of the effect of bank failures. Higherinterest rates cause more banks to become insolvent and run (because of decreasing assetsvalue). The excess demand will increase with interest rates if by failing, banks absorbmore liquidity than when solvent. Through these two channels (Fed interventions and firmsfailures), solvency risk has an aggregate endogenous feedback on the level of interest rates.

Mortgage growth (MTG) increases the demand for short-term debt. MTG is referredin Fontaine and Garcia (2012) as a factor exclusively affecting the demand for liquidityby increasing the pool of illiquid assets in the economy. Other considered factors includeflight-to-quality variables related to Money Market Mutual Funds (MMMF). The growthin MMMF assets (MMG) increases the supply of funding to banks via the shadow bankingsector (Adrian and Shin (2009); Fontaine and Garcia (2012)), but short-term funding supplydecreases when MMMF assets are allocated to safer assets like time deposits (MMA1) orgovernment-sponsored securities (MMA2).

The coefficient associated with MMA1 is negative and significant at the 1%. This resultcould, however, simply reflect the increase of the deposit insurance limit of the FederalDeposit Insurance Corporation (FDIC) in 2008Q4. Acharya and Mora (2013) document theshift from time deposits and debt issued by banks (and MMA1) to government-sponsoredsecurities (and MMA2), and the “liquidity reversal” in 2008Q4 where MMA1 started toincrease again. When the FDIC deposit insurance limit increased from 100K to 250K in thefourth quarter of 2008, uninsured deposits included in short-term debt shifted to the long-term part of the balance sheet. Therefore, the negative impact of MMA1 on banks’ short-term debt partly corresponds to the reallocation in 2008Q4 of some previously uninsuredtime deposits to the long-term debt within banks’ balance sheets.

We also note the positive coefficient of the VIX as banks’ exposure to short-term debt wasthe highest when the VIX peaked during the financial crisis. Finally, short-term assets arenot sensitive to any of the considered factors. While the level of short-term assets adjuststo shocks in other parts of the balance sheet, it is not directly affected by financial andmacroeconomic conditions.

17

3.3.3 Robustness of the solvency-liquidity nexus to common factors

I test the robustness of the solvency-liquidity nexus to the presence of common factors in

wit = αi + φi � wit−1 + θit+ λ′git−1 + β′ft−1 + εit (8)

where wit = (yit, zit, NetIncomeit/TAit, SRISKit/TAit)′, git is a ((2 ∗ K + 1) × 1) vector

stacking wit, wit ∗ sit and sit in a single column, λ is a ((2 ∗K + 1)× 1) vector containing theδ, γ and ω parameters, and ft is the vector of macroeconomic and financial factors identifiedin Section 3.3.2.

Chudik and Pesaran (2013) propose an alternative modeling strategy based on the Com-mon Correlated Effects (CCE) of Pesaran (2006) where the unobserved common factors areproxied by the cross-sectional averages of the dependent variable and the regressors

wit = αi + φi � wit−1 + θit+ λ′git−1 +1∑

l=0

ϕ′lwt−l + κ′gt−1 + εit (9)

where wt−l = N−1∑N

i=1wit−l and gt = N−1∑N

i=1 git.The estimation results of eq. (8) and eq. (9) are reported in Table 7. The fit improves

considerably when common factors are included. The best in-sample performance is foundwith the CCE model for all elements of wit. However, the CCE model counts a contempora-neous factor (average of the dependent variable) while the model with macro and financialfactors only includes lagged factors. The macro-financial model is therefore more convenientfor forecasting and the loss of in-sample fit is relatively small compared to the CCE model.

The solvency-liquidity nexus holds when I control for cross-sectional dependence. Theinteraction term between the profitability and SRISK is however not as important (notsignificant at the 5%). The impulse response functions do not qualitatively change eitherwhen macroeconomic and financial factors are considered.

3.3.4 Short-term debt components and long-term leverage

The different components of short-term debt (repos, uninsured deposits, commercial papers,etc.) have very different characteristics and may not react to solvency risk with the samemagnitude. Table 12 (Appendix C) reports the parameter estimates of eq. (4) where thedependent variable in each column is a different component (in logarithm) of the short-termdebt available from FR 9-YC reports. SRISK predicts most of the components of theshort-term debt; it is significant at the 1% level for wholesale funding (Fed funds, repos,

18

and commercial papers), and at the 5% level for retail funding (uninsured time deposits andforeign office deposits).

The expected capital shortfall SRISK is only related to the short-term part of thebalance sheet and does not predict long-term leverage. Table 8 shows that the long-termbalance sheet is not related to SRISK. The long-term debt only reacts to short-term assetsand the change in long-term assets.

Other robustness checks (not reported in this paper) show that the interaction betweensolvency and liquidity remains with homogenous dynamic parameters (φi = φ, ∀i), homoge-nous trend parameters (θi = θ, ∀i), without trend (θi = 0, ∀i), and when a break in 2008Q4is included in the trend. These results tend to confirm the robustness of the solvency-liquidity nexus. In the next section, I test for the out-of-sample forecasting performance ofthe solvency-liquidity nexus in predicting the short-term balance sheet of banks.

4 Forecasting the short-term balance sheet

To test for the out-of-sample predictive performance of the solvency-liquidity nexus, I con-duct two forecasting exercises. Both exercises are based on a fixed estimation period from2000Q1 to 2010Q4 to forecast the balance sheet of banks over the four quarters of 2011. Theinformation is updated each quarter in the one-step ahead forecasts (wit+1|t), while there isno information update in the dynamic forecasts (wit+h|t). The out-of-sample period corre-sponds to the European sovereign debt crisis, funding conditions were not as tight as duringthe financial crisis in the US but there is a total decline of $161 billion in short-term fundingof US banks during this period.

The root-mean square forecasting error (RMSFE) of the one-step ahead forecasting exer-cise are reported in Table 9. In this Table, I report the RMSFE of the short-term debt andshort-term assets individually (Panel A and B), as well as the RMSFE of their difference(Panel C). As already mentioned, the liquid asset shortfall is a measure of the exposure ofbanks to funding liquidity risk; the wider the gap in the short-term balance sheet, the morevulnerable the bank to runs. As this paper studies the liquidity-solvency nexus of banks,I also report the RMSFE of this liquid asset shortfall for capital-constrained (Panel D) vs.adequately capitalized banks (Panel E).

Four models are considered: a univariate autoregressive model (AR), the panel VARmodel of eq. (4) (VAR), the panel VAR model of eq. (5) that allows for the interaction ofbank characteristics with the state variable sit = 1{SRISKit>0} (INT), and the model including

19

all these features together with the macroeconomic and financial factors (eq. (8)) (CF).The assumption on the trend appears to be the most important model characteristic to

impact forecasting errors. To check for the robustness of the forecasting results, I report theRMSFE of these models for different trend assumptions (heterogeneous trends, homogenoustrend, no trend, and a break in the homogenous trend in 2008Q4).

For the one-step ahead forecasts, the best model is the panel VAR model that accountsfor the interaction of bank characteristics with SRISK (INT), and that assumes a breakin the trend in the fourth quarter of 2008. When the trend parameters are constant overtime, the model with common factors (CF) performs the best for the liquid asset shortfall ascommon factors reflect the changing aggregate funding conditions after the financial crisis.In the last three columns of Table 7, I report the increase in RMSFE when a particular bankvariable is not included in the panel VAR model.This Table shows that omitting SRISKincreases the forecasting errors of the liquid asset shortfall considerably, and particularly forcapital constrained banks during 2011. However, the panel VAR model or the interactionwith solvency risk (INT) does not improve the forecasts of adequately capitalized banks.

I obtain very similar results for the dynamic forecasts and therefore do not report theirRMSFE. Note that the RMSFE of dynamic forecasts are larger compared to the errors ofone-step ahead forecasts due to the absence of information updates over the forecastinghorizon. The model with interaction with SRISK (INT) and a break in the trend afterthe financial crisis is also the preferred model according the RMSFE of dynamic forecasts.The cross-sectional average dynamic forecasts obtained with this model for the short-termbalance sheet levels and flows over 2011Q1-2013Q1 are illustrated in Figure 7. It turns outthat the model is outstanding at forecasting short-term financing flows but does a less goodjob at forecasting short-term asset flows, which are not sensitive to the factors considered inthe model.

In Figure 8, I show the average dynamic forecasts of the liquid asset shortfall across allbanks, as well as for the subsamples of capital-constrained vs. adequately capitalized banks.As mentioned in the introduction, the liquid asset shortfall of capital-constrained banksspiked in the first quarters of 2007 and suddenly dropped afterwards due to the suddenfreeze of short-term funding markets. In the first quarter of 2011, the average liquid assetshortfall of capital-constrained banks became negative; capital-constrained firms had lessexposure to funding liquidity risk than adequately capitalized banks for the first time overthe sample period. The model predicts this reversal in the solvency-liquidity nexus andpredicts well the average excess of liquidity of capital-constrained banks during this period.

20

5 Conclusion

This paper reveals the empirical solvency-liquidity nexus of banks. While the interactionbetween solvency and liquidity has been well studied in the theoretical economic literature,this relationship tends to be omitted in the new capital and liquidity regulatory standardsintroduced under Basel III. In this paper, I test the solvency-liquidity nexus by examiningthe short-term balance sheet and the solvency risk measures of a sample of US bank holdingcompanies over 2000-2013.

I find that the expected capital shortfall of a bank in a crisis (SRISK) predicts how muchshort-term funding the bank has access to. Conversely, when the bank holds more short-termdebt, its risk of insolvency in a crisis increases. This result appears to be strong under manyrobustness checks and supports the theoretical models of the interaction between solvencyand liquidity risks and its amplification (aggregate) effects leading to systemic risk.

Importantly, not all solvency risk measures predict the bank’s access to short-term debt.The expected capital shortfall SRISK interacts well with the level of short-term funding ofthe bank compared to other solvency risk measures because (i) it is a measure of the bank’sexposure to aggregate risk, and (ii) it combines both book and market values. Suppliers ofliquidity are mostly concerned with the vulnerability of the bank to an aggregate crisis dueto the high liquidation costs the distressed bank will face in the presence of fire sales. Whenthe crisis happens, ’pure’ solvency risk (measured by the Tier 1 leverage ratio) amplified bymarket shocks explains the bank access to short-term funding.

The expected capital shortfall of the bank under stress also interacts with its profitabilityin determining its short-term balance sheet. While a profitable bank gets a larger accessto short-term funding and does not hold as much liquid assets, the impact of the bank’sprofitability on its liquidity profile tends to disappear when the bank is expected to becapital-constrained in a crisis.

The solvency-liquidity nexus provides useful information for forecasting the short-termfinancing flows during 2011 (European sovereign debt crisis). I show that the forecastingerrors of the liquid asset shortfall of banks increase considerably when the stressed solvencyrisk measure is not included in the regression.

Overall, the results of this paper suggest that the solvency-liquidity nexus should beaccounted for when designing liquidity monitoring tools and prudential requirements. Thisfinding contrasts with Basel regulation where solvency and liquidity risks are treated sepa-rately and gives empirical support for an additional capital requirement for banks with largeexposure to short-term funding.

21

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Dep. variable: yit zit (SRISK/TA)it(SRISK/TA)it−1 -1.120** 0.074

(0.244) (0.114)

zit−1 -0.040 -0.001(0.023) (0.002)

yit−1 -0.003 0.009**(0.022) (0.002)

R2 (%) 20.811 22.157 15.151Adj. R2 (%) 15.430 16.868 9.429

Table 1: Testing the solvency-liquidity nexus. Estimates from pooled OLS regressionwith bank dummies, time trends, and heterogeneous AR parameters. Dependent variables:yit = ln(STDebtit), zit = ln(STAssetsit), (SRISK/TA)it = SRISKit/TotalAssetsit. Ro-bust standard errors in parentheses. * significant parameter at 5%; ** at 1%. Sample: 2107panel obs. over 2000Q1-2013Q1 (unbalanced), 44 banks. SRISK is the expected capitalshortfall of the bank in a crisis.

25

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Dep.variab

le:

y it

z it

y it

z it

y it

z it

y it

z it

y it

z it

y it

z it

y it

z it

T1C

Rit−

10.301

-0.070

0.041

-0.089

(0.337)

(0.134)

(0.552)

(0.360)

T1L

VGR

it−

10.508

-0.074

-1.148

-0.142

(0.491)

(0.305)

(0.875)

(0.832)

RealV

olit−

1-0.438

0.919*

2.286*

0.151

(0.412)

(0.450)

(1.119)

(1.491)

ES i

t−1

-0.250

0.412

-0.697*

0.364

(0.159)

(0.203)

(0.397)

(0.644)

DCB

it−

1-0.046

0.030

-0.021

0.002

(0.027)

(0.034)

(0.028)

(0.040)

4CoV

aRit−

1-0.402

0.188

0.094

0.102

(0.761)

(0.784)

(0.750)

(0.801)

(SRISK/T

A) i

t−1

-1.579**

-0.078

(0.072)

(0.141)

MB

it−

10.042

-0.014

0.042

-0.014

0.035

-0.001

0.033

0.000

0.036

-0.011

0.041

-0.015

-0.053**

-0.005

(0.026)

(0.017)

(0.025)

(0.017)

(0.027)

(0.017)

(0.026)

(0.017)

(0.025)

(0.019)

(0.024)

(0.017)

(0.017)

(0.022)

R2(%

)16.621

22.196

16.604

22.192

16.581

22.393

16.623

22.424

16.645

22.235

16.542

22.194

21.461

22.428

Adj.

R2(%

)10.955

16.909

10.937

16.905

10.913

17.119

10.957

17.153

10.980

16.951

10.871

16.907

15.868

16.904

Table2:

Testingalternativesolven

cyrisk

measures.

Estim

ates

from

pooled

OLS

regression

withba

nkdu

mmies,

timetrends

andheterogeneou

sAR

parameters.

Dep

endent

variab

les:y i

t=

ln(STDebt i

t),z i

t=

ln(STAssets i

t).T1C

R:

Tier1Com

mon

Cap

ital

Ratio,T

1LVGR:T

ier1Le

verage

Ratio,R

ealVol:Realized

volatility,

DCB:D

ynam

icCon

dition

alBeta(E

ngle

(201

2)),SRISK/TA

=SR

ISK/T

otal

Assets,

MB:m

arketto

book

equity

ratio.

Rob

uststan

dard

errors

inpa

rentheses.

*sign

ificant

parameter

at5%

;**

at1%

.Sa

mple:

2107

panelob

s.over

2000

Q1-20

13Q1(unb

alan

ced),44

bank

s.

26

(1)

(2)

(3)

(4)

(5)

(6)

Dep.variab

le:

y it

z it

y it

z it

y it

z it

y it

z it

y it

z it

y it

z it

(SRISK/T

A) i

t−1

-1.439**

0.010

(0.105)

(0.110)

LRMES i

t−1

-0.162

0.205

-0.080

0.195

(0.096)

(0.111)

(0.110)

(0.117)

Lvg i

t−1

-0.002

0.001

-0.002

0.000

(0.001)

(0.001)

(0.001)

(0.001)

(MV/T

A) i

t−1

0.930**

-0.002

0.925**

0.002

(0.051)

(0.049)

(0.052)

(0.046)

(SMV/T

A) i

t−1

1.369**

-0.021

(0.080)

(0.116)

MB

it−

1-0.048**

-0.014

0.032

-0.002

0.032

-0.007

-0.050**

-0.014

-0.051**

-0.013

-0.060

-0.001

(0.016)

(0.022)

(0.025)

(0.019)

(0.027)

(0.019)

(0.019)

(0.021)

(0.016)

(0.022)

(0.020)

(0.024)

R2(%

)21.110

22.191

16.714

22.443

16.701

22.254

20.725

22.191

21.338

22.192

20.931

22.446

Adj.

R2(%

)15.749

16.904

11.055

17.173

11.041

16.971

15.338

16.903

15.993

16.905

15.473

17.092

Table3:

TestingSRISK

compon

ents.Estim

ates

from

pooled

OLS

regression

withba

nkdu

mmies,

timetrends

and

heterogeno

usAR

parameters.

Dep

endent

variab

les:y i

t=

ln(STDebt i

t),z

it=

ln(STAssets i

t).MV:m

arketcapitalization,

TA:total

assets,R

ealVol:Realized

volatility,SRISK/TA

=SR

ISK/T

otal

Assets,LR

MES:

Long

-Run

Margina

lExp

ected

Shortfall,Lv

g:qu

asi-m

arketleverage,M

B:m

arketto

book

equity

ratio,

SMV/T

A=

MV*(1-LR

MES)/T

A.R

obuststan

-da

rderrors

inpa

rentheses.

*sign

ificant

parameter

at5%

;**

at1%

.Sa

mple:

2107

panelob

s.over

2000

Q1-20

13Q1

(unb

alan

ced),4

4ba

nks.

27

Pan

elA

:N

oin

tera

ctio

nw

iths i

t=

1 {S

RIS

Kit

>0}

Pan

elB

:In

tera

ctio

nw

iths i

t=

1 {S

RIS

Kit

>0}

Dep

.va

riab

le:

y it

z it

(NI/

TA

) it

(SR

ISK

/TA

) it

y it

z it

(NI/

TA

) it

(SR

ISK

/TA

) it

(SR

ISK

/TA

) it−

1-1

.063

**-0

.028

-2.2

25**

-0.9

35**

-0.1

20-1

.681

**(0

.245

)(0

.118

)(0

.301

)(0

.261

)(0

.101

)(0

.080

)(S

RIS

K/T

A) i

t−1∗

s it−

1-0

.408

1.75

7*-5

.871

**(0

.751

)(0

.767

)(1

.767

)

(NI/

TA

) it−

12.

354

-4.2

28-1

.217

**9.

704*

*-7

.944

*-2

.809

**(2

.278

)(2

.331

)(0

.389

)(3

.290

)(3

.716

)(0

.935

)(N

I/TA

) it−

1∗

s it−

1-9

.902

*6.

315

2.13

4*(4

.396

)(5

.183

)(0

.937

)

zit−

1-0

.038

-0.0

15-0

.002

-0.0

33-0

.035

-0.0

01(0

.023

)(0

.020

)(0

.002

)(0

.022

)(0

.022

)(0

.003

)z

it−

1∗

s it−

1-0

.021

*0.

078*

-0.0

008

(0.0

08)

(0.0

32)

(0.0

02)

yit−

1-0

.004

-0.0

67**

0.00

8**

-0.0

02-0

.031

0.00

8**

(0.0

21)

(0.0

26)

(0.0

02)

(0.0

22)

(0.0

21)

(0.0

02)

yit−

1∗

s it−

1-0

.007

*-0

.080

*0.

002

(0.0

10)

(0.0

32)

(0.0

02)

s it−

10.

347*

0.06

60.

094

-0.0

18(0

.144

)(0

.159

)(0

.187

)(0

.018

)

R2

(%)

20.8

7022

.318

41.9

2515

.787

21.2

7822

.562

44.4

7416

.184

Adj

.R

2(%

)15

.450

16.9

9737

.977

10.0

6215

.715

17.0

8940

.579

10.3

04

Table4:

Testingtheinteraction

between

solven

cyan

dprofitability.

Estim

ates

from

pooled

OLS

regression

withba

nkdu

mmies,

timetrends,an

dheterogeneou

sAR

parameters.

Pan

elA:mod

elof

eq.(5)witho

utstatevariab

le.

Pan

elB:mod

elof

eq.

(5)with

statevariab

les i

t=

1 {S

RIS

Kit

>0}.

Dep

endent

variab

les:

y it

=ln

(STDebt i

t),z i

t=

ln(STAssets i

t),(NI/TA

) it

=NetIncome i

t/TotalAssets i

t,(SRISK/TA

) it

=SRISK

it/TotalAssets i

t.Rob

uststan

dard

errors

inpa

rentheses.

*sign

ificant

parameter

at5%

;**at

1%.Sa

mple:

2107

panelo

bs.over

2000

Q1-20

13Q1(unb

alan

ced),

44ba

nks.

SRISK

istheexpe

cted

capitals

hortfallof

theba

nkin

acrisis.

28

CPP/TA TLGP/TACst 4.280 -7.478

(6.088) (8.948)

T1LVGR 0.222 -0.941*(0.269) (0.395)

T1CR -0.285* 0.181(0.106) (0.155)

log(TA) -0.042 0.806*(0.240) (0.352)

R2 (%) 37.701 72.217Adj. R2 (%) 23.325 65.805

Table 5: Testing factors explaining capital and liquidity injections under theTARP. Estimates from cross-sectional OLS regression. Dependent variables: the amountof capital received under the CPP divided by total assets (CPP/TA), the amount of totalunsecured debt guaranteed by the FDIC divided by total assets (TLGP/TA). T1LVGR: Tier1 Leverage ratio, T1CR: Tier 1 Common Capital Ratio, log(TA): logarithm of total assets,as of 2008Q2. Robust standard errors in parentheses. * significant parameter at 5%; ** at1%. Sample: 17 banks.

29

Dep. variable: yit zit (NI/TA)it (SRISK/TA)itFedfund ratet−1 0.045** 0.001 -0.031 -0.005

(0.011) (0.014) (0.019) (0.003)

Treasury slopet−1 0.077** 0.013 -0.055 0.006**(0.023) (0.026) (0.029) (0.001)

TEDt−1 0.003 0.043 -0.172** 0.009*(0.015) (0.024) (0.048) (0.004)

VIXt−1 0.003** 0.0004 -0.002 -0.00005(0.001) (0.001) (0.001) (0.0002)

M2Gt−1 -4.308** -0.366 0.255 0.154(1.351) (1.035) (1.078) (0.171)

MTGt−1 3.760** -1.281 0.946 -0.748*(1.120) (1.455) (1.236) (0.368)

MMGt−1 0.463** -0.308 -0.197 0.008(0.172) (0.223) (0.336) (0.034)

MMA1t−1 -1.994** 1.058 -0.592 -0.300**(0.455) (0.601) (0.628) (0.073)

MMA2t−1 0.265 -0.291 -1.510** -0.181*(0.222) (0.383) (0.509) (0.086)

R2 (%) 21.996 23.816 44.559 19.217Adj. R2 (%) 16.399 18.350 40.609 13.461

Table 6: Testing common factors. Estimates from pooled OLS regression with bankdummies, time trends, heterogeneous AR parameters and common factors. Robust standarderrors in parentheses. * significant parameter at 5%; ** at 1%. Sample: 2107 panel obs. over2000Q1-2013Q1 (unbalanced), 44 banks. Treasury slope is the slope factor of the Treasuryyield curve. M2G: money supply growth (M2). MTG: mortgage assets growth. MMG:MMMF assets growth. MMA1: proportion of MMMF assets allocated to time deposits.MMA2: proportion of MMMF assets allocated to Treasury, agency, or municipal bonds.

30

NoCom

mon

Factor

Com

mon

Factors

Com

mon

CorrelatedEffe

cts

Dep

.va

riab

le:

yit

z it

NI/

TA

SRIS

K/T

Ay

itz i

tN

I/TA

SRIS

K/T

Ay

itz i

tN

I/TA

SRIS

K/T

A

(SR

ISK

/TA

) it−

1-0.935**

-0.120

-1.681**

-0.847**

-0.178

-1.417**

-0.900**

-0.137

-1.649**

(0.261)

(0.101)

(0.080)

(0.318)

(0.096)

(0.117)

(0.280)

(0.106)

(0.093)

(SR

ISK

/TA

) it−

1∗

s it−

1-0.408

1.757*

-5.871**

-0.687

1.291

-5.108**

-1.413

2.384*

-5.250**

(0.751)

(0.767)

(1.767)

(0.853)

(0.861)

(1.736)

(0.974)

(1.009)

(1.976)

(NI/

TA

) it−

19.704**

-7.944*

-2.809**

8.111*

-7.564*

-2.639*

8.512*

-7.964*

-2.205**

(3.290)

(3.716)

(0.935)

(3.677)

(3.575)

(1.026)

(3.542)

(3.905)

(0.771)

(NI/

TA

) it−

1∗

s it−

1-9.902*

6.315

2.134*

-8.087

4.817

2.034*

-7.181

7.926

2.105*

(4.396)

(5.183)

(0.937)

(4.788)

(4.920)

(0.976)

(4.655)

(5.512)

(0.826)

zit−

1-0.033

-0.035

-0.001

-0.008

-0.047*

-0.004

0.0004

-0.045

-0.004

(0.022)

(0.022)

(0.003)

(0.024)

(0.024)

(0.003)

(0.024)

(0.024)

(0.003)

zit−

1∗

s it−

1-0.021*

0.078*

-0.0008

-0.018*

0.052*

0.0003

-0.013

0.047

0.0006

(0.008)

(0.032)

(0.002)

(0.008)

(0.025)

(0.002)

(0.008)

(0.025)

(0.001)

yit−

1-0.002

-0.031

0.008**

0.002

0.015

0.009**

0.004

0.026

0.008**

(0.022)

(0.021)

(0.002)

(0.002)

(0.018)

(0.003)

(0.020)

(0.018)

(0.003)

yit−

1∗

s it−

1-0.007*

-0.080*

0.002

-0.010

-0.051*

-0.001

-0.013

-0.046*

-0.003

(0.010)

(0.032)

(0.002)

(0.009)

(0.022)

(0.002)

(0.010)

(0.022)

(0.002)

s it−

10.347*

0.066

0.094

-0.018

0.327*

0.098

0.034

0.011

0.253

0.148

0.014

0.029

(0.144)

(0.159)

(0.187)

(0.018)

(0.140)

(0.154)

(0.139)

(0.016)

(0.140)

(0.158)

(0.145)

(0.017)

R2(%

)21.278

22.562

44.474

16.184

25.079

24.247

48.438

20.665

26.730

27.265

50.295

30.990

Adj.

R2(%

)15.715

17.089

40.579

10.304

19.416

18.521

44.567

14.709

21.192

21.767

46.564

25.809

Table7:

Rob

ustnessof

thesolven

cy-liquiditynexusto

common

factors.

Estim

ates

from

pooled

OLS

regres-

sion

with

bank

dummies,

timetrends,heterogeneou

sAR

parametersan

dstatevariab

les i

t=

1 {S

RIS

Kit

>0}.

Dep

en-

dent

variab

les:y i

t=

ln(STDebt i

t),z i

t=

ln(STAssets i

t),

(NI/TA

) it

=NetIncome i

t/TotalAssets i

t,(SRISK/TA

) it

=SRISK

it/TotalAssets i

t.NoCom

mon

Factor:regression

witho

utcommon

factors(eq.

(5)).Com

mon

Factors:

regression

withall(

lagg

ed)common

factorsof

Table6(eq.

(8)).Com

mon

CorrelatedEffe

cts:

regression

withcommon

correlated

effects

(eq.

(9)).Rob

uststan

dard

errors

inpa

rentheses.

*sign

ificant

parameter

at5%

;**

at1%

.Sa

mple:

2107

panel

obs.

over

2000

Q1-20

13Q1(unb

alan

ced),4

4ba

nks.

SRISK

istheexpe

cted

capitals

hortfallof

theba

nkin

acrisis.

31

Dep. variable: dYit dZit yit zit (NI/TA)it (SRISK/TA)it

(SRISK/TA)it−1 -0.013 -0.039 -1.059** -0.038 -2.241**(0.024) (0.038) (0.235) (0.118) (0.282)

(NI/TA)it−1 -0.870 0.290 2.313 -4.185 -1.211**(0.592) (0.508) (2.232) (2.348) (0.386)

zit−1 -0.035** -0.006 -0.034 0.162 -0.002(0.005) (0.006) (0.024) (0.162) (0.002)

yit−1 -0.0004 -0.018** -0.002 -0.023 0.008**(0.006) (0.006) (0.022) (0.021) (0.002)

dZit−1 0.101* 0.004 -0.110 -0.103 0.014(0.046) (0.109) (0.116) (0.145) (0.012)

dY it−1 -0.104* -0.137 0.157 0.254 -0.002(0.052) (0.199) (0.096) (0.224) (0.011)

R2 (%) 11.319 12.008 21.047 22.411 42.099 15.837Adj. R2 (%) 5.197 5.934 15.554 17.013 38.099 10.024

Table 8: Estimates from pooled OLS regression with bank dummies, time trends and het-erogeneous AR parameters. Dependent variables: dYit = ln(LTDebtit/LTDebtit−1), dZit =ln(LTAssetsit/LTAssetsit−1), yit = ln(STDebtit), zit = ln(STAssetsit), (NI/TA)it =NetIncomeit/TotalAssetsit, (SRISK/TA)it = SRISKit/TotalAssetsit. Robust standarderrors in parentheses. * significant parameter at 5%; ** at 1%. Sample: 2107 panel obs.over 2000Q1-2013Q1 (unbalanced), 44 banks. SRISK is the expected capital shortfall of thebank in a crisis.

32

PA

NEL

A:Fo

reca

stin

gth

esh

ort-

term

deb

tTrend

assumption

AR

VAR

INT

CF

4RMSF

E(SRISK)4RMSF

E(N

I)4RMSF

E(STA)

heterogeneou

strends

1856

716

338

1626

711

939

1871

-236

451

homogenou

strend

1023

910

577

7943

1075

381

3-5

19-1

98no

trend

8438

7943

6801

9046

1165

-185

-78

trendbreak

1003

882

9575

8112

986

1252

-43

-148

PA

NEL

B:Fo

reca

stin

gth

esh

ort-

term

asse

tsTrend

assumption

AR

VAR

INT

CF

4RMSF

E(SRISK)4RMSF

E(N

I)4RMSF

E(STA)

heterogeneou

strends

1307

913

817

1359

615

011

-113

84-8

02ho

mogenou

strend

1347

713

828

1357

014

381

45-1

27-2

28no

trend

1463

215

349

1448

314

176

370

-192

-651

trendbreak

1323

513

108

1298

813

985

-60

-101

264

PA

NEL

C:Fo

reca

stin

gth

eliqu

idas

set

shor

tfal

l(w

hol

esa

mple

)Trend

assumption

AR

VAR

INT

CF

4RMSF

E(SRISK)4RMSF

E(N

I)heterogeneou

strends

1983

417

374

1567

313

426

1638

-301

homogenou

strend

1573

718

475

1689

115

244

370

-791

notrend

1599

917

172

1595

214

915

1629

-576

trendbreak

1435

314

159

1399

315

782

225

-321

PA

NEL

D:Fo

reca

stin

gth

eliqu

idas

set

shor

tfal

lof

adeq

uat

ely

capit

aliz

edban

ks(S

RIS

Kit≤

0)Trend

assumption

AR

VAR

INT

CF

4RMSF

E(SRISK)4RMSF

E(N

I)heterogeneou

strends

7702

6443

6992

4927

87-2

7ho

mogenou

strend

5294

6003

6672

5338

-185

-84

notrend

5297

6117

6666

5725

-58

-54

trendbreak

4431

5374

5654

5081

-236

-49

PA

NEL

E:Fo

reca

stin

gth

eliqu

idas

set

shor

tfal

lof

capit

al-c

onst

rain

edban

ks(S

RIS

Kit

>0)

Trend

assumption

AR

VAR

INT

CF

4RMSF

E(SRISK)4RMSF

E(N

I)heterogeneou

strends

2541

322

329

1985

817

267

2214

-406

homogenou

strend

2033

723

916

2161

519

658

536

-105

7no

trend

2069

222

122

2032

619

125

2226

-774

trendbreak

1862

418

170

1787

720

439

358

-429

Table9:

Forecastingtheshort-term

balan

cesheet.

Roo

tMean

Squa

reFo

recastingError

(RMSF

E):

one-step

aheadforecastingover

2011

.Fixed

estimationsample(200

0-20

10),

inform

ationup

datedeach

quarter.

AR:un

ivariate

autoregressive

mod

el.VA

R:pa

nelVA

Rmod

el(eq.

(4)).IN

T:pa

nelVA

RwithinteractionwithSR

ISK

(eq.

(5)).CF:

panelV

ARwithinteractionwithSR

ISK

andcommon

factors(eq.

(8)).4RMSE

(x)istheincrease

inRMSE

whenvariab

lexis

notinclud

edin

theVA

Rmod

el.Liqu

idassetshortfall=

STDebt-ST

Assets.

Inbo

ld:minim

umRMSF

Eforeach

line(trend

assumption).

33

STAssets STDebt STAssetsSTDebt

LTAssets LTDebtLTAssets LTDebt

EquityEquity

Bank is balance-sheet insolvent.Assets are liquidated at a loss, only senior creditors are repaid.

STDebt

LTAssetsLTDebt

Figure 1: Simplified balance sheet. Liquid asset shortfallit = STDebtit−STAssetsit. Capitalshortfallit = k ∗ (STAssetsit +LTAssetsit)−Equityit. Expected capital shortfall in a crisisSRISKit = E [k ∗ (STAssetsit+h + LTAssetsit+h)− Equityit+h|crisist+h] = k∗(LTDebtit +STDebtit) − (1 − k) ∗ Equityit ∗ (1 + E(Rit+h|crisist+h)), where k is the prudential capitalratio (8%).

34

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

0

25000

50000

75000

100000

125000

Av

erag

e li

qu

id a

sset

sh

ort

fall

($

m)

Avg(STDebt ­ STAssets) if SRISK<0 Avg(STDebt ­ STAssets) if SRISK>0

#firms (SRISK<0) #firms (SRISK>0)

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

20

40#firms (SRISK<0) #firms (SRISK>0)

Figure 2: Cross-sectional average of the liquid asset shortfall of capital-constrained banks(black line) vs. cross-sectional average of the liquid asset shortfall of adequately capitalizedbanks (dashed line). Liquid asset shortfall = Short-term debt - Short-term assets ($m).“Adequately capitalized” means SRISKit ≤ 0.

35

Avg(STDebt) Avg(STAssets)

2000 1 2 3 4 5 6 7 8 9 10 11 12 13

20000

40000

60000

Avg(STDebt) Avg(STAssets)

Avg(STDebt ­ STAssets)

2000 1 2 3 4 5 6 7 8 9 10 11 12 13

­10000

0

10000

20000

30000

40000 Avg(STDebt ­ STAssets)

Avg(LTDebt) Avg(LTAssets) Avg(TotalAssets)

2000 1 2 3 4 5 6 7 8 9 10 11 12 13

100000

150000

200000

250000

300000 Avg(LTDebt) Avg(LTAssets) Avg(TotalAssets)

Avg(NetIncome)

2000 1 2 3 4 5 6 7 8 9 10 11 12 13

­500

0

500

Avg(NetIncome)

Figure 3: Cross-sectional averages of the balance sheet (in $m): short-term debt andshort-term assets (top-left panel), difference between short-term debt and short-term assets(top-right panel), total assets and long-term balance sheet (bottom-left panel), net income(bottom-right panel).

36

Avg(T1CR)

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

0.10

0.12

0.14Avg(T1CR)

Avg(T1LVGR)

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

0.08

0.09

0.10Avg(T1LVGR)

Avg(SRISK) ($m) Avg(max(0,SRISK)) ($m)

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

0

10000Avg(SRISK) ($m) Avg(max(0,SRISK)) ($m)

Figure 4: Cross-sectional averages of solvency risk measures. T1CR is the Tier 1 commoncapital ratio (Tier 1 common capital divided by risk-weighted assets); T1LVGR is the Tier 1leverage ratio (Tier 1 capital divided by total assets); SRISK is the expected capital shortfallin a crisis.

37

0 5 10

1

3NI ­> NI

0 5 10

­2

­1

0

1SRISK ­> NI

0 5 10

­1.0

­0.5

0.0STD ­> NI

0 5 10

­0.1

0.0

0.1

STA ­> NI

0 5 10

­0.4

­0.2

0.0

NI ­> SRISK

0 5 10

0.0

0.5

1.0

SRISK ­> SRISK

0 5 10

0.1

0.2

0.3STD ­> SRISK

0 5 10

­0.03

­0.01

STA ­> SRISK

0 5 10

0.5

1.0

1.5

2.0NI ­> STD

0 5 10

­4

­2

0SRISK ­> STD

0 5 10

0

5

10STD ­> STD

0 5 10

­0.50

­0.25

0.00STA ­> STD

0 5 10

­1.0

­0.5

0.0NI ­> STA

0 5 10

0.1

0.2

0.3SRISK ­> STA

0 5 10

0.0

0.1

0.2

0.3STD ­> STA

0 5 10

2.5

5.0

7.5

STA ­> STA

Figure 5: Impulse response functions. Median impulse response function (black lines) be-tween the 25% and 75% impulse response quantiles (dotted lines).

38

0 5 10

0

1

2

NI ­> NI

0 5 10

­5

0SRISK ­> NI

0 5 10

­1.0

­0.5

0.0STD ­> NI

0 5 10

0.0

0.5

STA ­> NI

0 5 10

­0.50

­0.25

0.00

NI ­> SRISK

0 5 10

0.25

0.75

SRISK ­> SRISK

0 5 10

0.10

0.15

STD ­> SRISK

0 5 10

­0.03

­0.01STA ­> SRISK

0 5 10

1

2

NI ­> STD

0 5 10

­4

­2

SRISK ­> STD

0 5 10

2.5

5.0

7.5

STD ­> STD

0 5 10

­0.6

­0.4

­0.2

STA ­> STD

0 5 10

­1.0

­0.5

0.0NI ­> STA

0 5 10

­0.50

­0.25

0.00

0.25SRISK ­> STA

0 5 10

0.0

0.2STD ­> STA

0 5 10

2.5

5.0

7.5STA ­> STA

Figure 6: Impulse response functions with SRISK as a state variable (eq. (5)). Medianimpulse response function when SRISKit ≤ 0 (black line) and median impulse responsefunction when SRISKit > 0 (dashed line).

39

Actual Forecast

2005 2006 2007 2008 2009 2010 2011 2012 2013

30000

40000

50000

60000

70000

Avg(STDebt) ($m)

Actual Forecast

2005 2006 2007 2008 2009 2010 2011 2012 2013

20000

30000

40000

50000

60000

Avg(STAssets) ($m)

2005 2006 2007 2008 2009 2010 2011 2012 2013

­5000

0

5000

Avg(STDebt flows) ($m)

2005 2006 2007 2008 2009 2010 2011 2012 2013

­5000

0

5000

Avg(STAssets flows) ($m)

Figure 7: Forecasting the short-term balance sheet over 2011Q1-2013Q1: dynamic forecasts(panel VAR with SRISK as a state variable (eq. (5)), break in trend).

40

Actual Forecast

2005 2006 2007 2008 2009 2010 2011 2012 2013

­10000

0

10000

20000

30000

40000Avg(STDebt ­ STAssets) ($m)

Actual Forecast

SRISK<0 SRISK>0

2005 2006 2007 2008 2009 2010 2011 2012 2013

0

25000

50000

75000

100000

125000

Avg(STDebt ­ STAssets) ($m)

SRISK<0 SRISK>0

Figure 8: Forecasting the Liquid Asset Shortfall over 2011Q1-2013Q1: dynamic forecasts(panel VAR with SRISK as a state variable (eq. (5)), break in trend).

41

Appendix

A Short-term debt and short-term assets compositionComposition of the short term debt estimate (SNL definitions):

• Fed funds purchased: The gross dollar amount of funds borrowed in the form of imme-diately available funds under agreements or contracts that mature in one business dayor roll over under a continuing contract, regardless of the nature of the transaction orthe collateral involved. Includes securities sold under agreements to repurchase thatinvolve the receipt of immediately available funds and mature in one business day orroll over under a continuing contract.

• Repurchase agreements: The gross dollar amount of security repurchase agreementsthat mature in more than one business day, other than securities sold under repurchaseagreements to maturity, but including sales of participations in pools of securities thatmature in more than one business day.

• Brokered Deposits (< $100K, maturity ≤ 1 Year): Brokered deposits issued in de-nominations of less than $100,000 with a remaining maturity of one year or less andare held in domestic offices of commercial banks or other depository institutions thatare subsidiaries of the reporting bank holding company. Remaining maturity is theamount of time remaining from the report date until the final contractual maturity ofa brokered deposit.

• Time Deposits (≥ $100K, maturity≤ 1Year): Time deposits issued in denominations of$100,000 or more with a remaining maturity of one year or less. Remaining maturity isthe amount of time remaining from the report date until the final contractual maturityof a time deposit.

• Foreign Office Time Deposits (maturity ≤ 1Year): All time deposits in foreign officeswith remaining maturities of one year or less. Remaining maturity is the amount oftime remaining from the report date until the final contractual maturity of a timedeposit.

• Commercial Paper: The total amount outstanding of commercial paper issued by thereporting bank holding company or its subsidiaries.

• Other borrowed money: The total amount of money borrowed by the consolidatedbank holding company with a remaining maturity of one year or less. For purposes ofthis item, remaining maturity is the amount of time remaining from the report dateuntil the final contractual maturity of a borrowing without regard to the borrowing’srepayment schedule, if any. Includes the dollar amount outstanding of all interest-bearing demand notes issued to the U.S. Treasury by the depository institutions thatare consolidated subsidiaries of the reporting bank holding company. Also includes

42

mortgage indebtedness and obligations under capitalized leases with a remaining ma-turity of one year or less. Also includes the total amount of money borrowed with aremaining maturity of one year or less: (1) on its promissory notes; (2) on notes andbills rediscounted; (3) on loans sold under repurchase agreements that mature in morethan one business day; (4) by the creation of due bills representing the bank holdingcompany’s receipt of payment and similar instruments, whether collateralized or un-collateralized; (5) from Federal Reserve Banks; (6) by overdrawing ’due from’ balanceswith depository institutions, except overdrafts arising in connection with checks ordrafts drawn by subsidiary depository institutions of the reporting bank holding com-pany and drawn on, or payable at or through, another depository institution either ona zero-balance account or on an account that is not routinely maintained with suffi-cient balances to cover checks or drafts drawn in the normal course of business duringthe period until the amount of the checks or drafts is remitted to the other depositoryinstitution; (7) on purchases of so-called ’term federal funds’; and (8) on any otherobligation for the purpose of borrowing money that has a remaining maturity of oneyear or less and that is not reported elsewhere.

0

500000

1000000

1500000

2000000

2500000

3000000

3500000

2000

Q1

2000

Q3

2001

Q1

2001

Q3

2002

Q1

2002

Q3

2003

Q1

2003

Q3

2004

Q1

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Q3

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Q1

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Q3

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Q1

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Q3

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200

8Q

1

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Q3

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Q1

2009

Q3

2010

Q1

2010

Q3

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Q1

2011

Q3

2012

Q1

2012

Q3

2013

Q1

14. Total fed funds & repurchase agreements 1. Brokered deposits < $100K with <= 1yr maturity

3. Time deposits >= $100K with <= 1yr maturity 4. Foreign office time deposits <= 1yr maturity

a. Commercial paper b. Other with maturity of < 1 year

Figure 9: Short term debt composition ($m) - 44 BHCs

43

Composition of the short term assets estimate (SNL definitions):

• Cash & Non interest-bearing Deposits: The total of all noninterest-bearing balancesdue from depository institutions, currency and coin, cash items in process of collection,and unposted debits. Includes balances due from banks in the U.S., banks in foreigncountries and foreign central banks, foreign branches of other U.S. banks, Federal HomeLoan Banks, and Federal Reserve Banks.

• Total Interest-bearing Balances: The total of all interest-bearing balances due fromdepository institutions and foreign central banks that are held in offices of the bankholding company or its consolidated subsidiaries.

• Fed Funds Sold: The gross dollar amount of funds lent in the form of immediatelyavailable funds under agreements or contracts that mature in one business day or rollover under a continuing contract. Includes securities purchased under agreements toresell that involve the receipt of immediately available funds and mature in one businessday or roll over under a continuing contract.

• Reverse Repurchases Agreements: The gross dollar amount of security resale agree-ments that mature in more than one business day, other than securities purchasedunder resale agreements to maturity, and of purchases of participations in pools ofsecurities that mature in more than one business day.

• Debt Securities Maturing or Repriced (maturity ≤ 1Year): All securities held by theconsolidated bank holding company with a remaining maturity or amount of timeremaining until next repricing date of one year or less. Held-to-maturity securitiesare reported at amortized cost and available-for-sale securities are reported at fairvalue. Remaining maturity is the amount of time remaining from the report date untilthe final contractual maturity of the instrument without regard to the instrument’srepayment schedule. Next repricing date is the date the interest rate on a floating ratedebt security can next change. (Y9 Line Item: BHCK0383)

44

0

500000

1000000

1500000

2000000

2500000

2000

Q1

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Q3

2001

Q1

2001

Q3

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Q1

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8Q

1

2008

Q3

2009

Q1

2009

Q3

2010

Q1

2010

Q3

2011

Q1

2011

Q3

2012

Q1

2012

Q3

2013

Q1

2. a. Debt securities: Maturity/Repricing <= 1Yr a. Cash & noninterest bearing balances

b. Total interest bearing balances 3. Tot fed funds & reverse repos

Figure 10: Short-term assets composition ($m) - 44 BHCs

45

B Stationarity of balance sheet aggregatesTo test for the stationarity of yit, zit and other balance sheet quantities, I apply the unit roottest of Pesaran (2007) (CIPS) robust to cross-sectional dependence between individuals inthe panel data set. The the null hypothesis is H0 : α21 = α22 = ... = α2N = 0, i = 1, 2, ..., N(unit root), and the alternative Ha : α21 < 0, ..., α2N0 < 0, N0 ≤ N(a significant fraction ofthe panel is stationary). The regression for the CIPS unit root test is

dyit = α0i + α1idyit−1 + α2iyit−1 + aidyt + biyt−1 + cidyt−1 + θit+ εit, (10)

where dyt = N−1∑N

i=1 dyit, yt = N−1∑N

i=1 yit. The CIPS test statistics are reported in Table10 for both cases with and without trend (i.e. θi = 0, ∀i). Based on the CIPS statistics andgiven the critical values of the CADF distribution, yit is stationary only when the regressionincludes a trend. The hypothesis of the absence of a trend is rejected based on a Wald test,therefore yit is considered stationary in the rest of the paper.

On the other bank sheet aggregates, the UR hypothesis is not rejected for the size (loga-rithm of total assets) and the long-term balance sheet (logarithm of long-term assets Zit andlong-term debt Yit). Finally, the short-term assets, SRISK and the net income divided bytotal assets are stationary with this test.

Intercept only Intercept and trendCIPS CIPSb CIPS CIPSb

yit -2.064 -1.922 -2.725 -2.660zit -2.538 -2.545 -2.798 -2.849

NIit/TAit -3.541 -3.831 -4.101 -4.381Yit -2.071 -2.199 -2.274 -2.468Zit -1.954 -2.098 -2.449 -2.584

log(TAit) -1.709 -1.932 -2.163 -2.336SRISKit/TAit -2.579 -2.434 -2.951 -2.989

Table 10: Panel UR tests: CIPS statistics. CADF 5% critical values: -2.11 (intercept only),-2.60 (intercept and trend). CIPSb is the CIPS statistic based on a balanced panel dataset.yit = ln(STDebtit), zit = ln(STAssetsit), Yit = ln(LTDebtit), Zit = ln(LTAssetsit), NIit:net income, TAit: total assets.

46

C Robustness checks

C.1 Period dummies

Dep. variable: yit zit (NI/TA)it (SRISK/TA)it yit zit (NI/TA)it (SRISK/TA)it

(SRISK/TA)it−1 -1.063** -0.028 -2.225** -0.623 -0.108 -2.033**(0.245) (0.118) (0.301) (0.357) (0.178) (0.217)

(SRISK/TA)it−1 ∗ ct -0.606** 0.188 -0.321(0.231) (0.167) (0.182)

(SRISK/TA)it−1 ∗ pct -0.091 -0.298 0.137(0.383) (0.262) (0.194)

(NI/TA)it−1 2.354 -4.228 -1.217** 25.036** -7.046 -7.529**(2.278) (2.331) (0.389) (7.838) (5.344) (2.011)

(NI/TA)it−1 ∗ ct -24.850** 5.882 6.355**(8.248) (6.315) (1.576)

(NI/TA)it−1 ∗ pct -20.939 -8.164 9.165**(12.332) (7.475) (2.463)

zit−1 -0.038 -0.015 -0.002 -0.012 -0.033 0.001(0.023) (0.020) (0.002) (0.024) (0.024) (0.002)

zit−1 ∗ ct -0.003 0.018 -0.006**(0.011) (0.033) (0.002)

zit−1 ∗ pct -0.008 0.003 -0.001(0.020) (0.030) (0.003)

yit−1 -0.004 -0.067** 0.008** 0.002 0.015 0.008*(0.021) (0.026) (0.002) (0.023) (0.017) (0.003)

yit−1 ∗ ct 0.011 -0.048 0.007*(0.014) (0.034) (0.003)

yit−1 ∗ pct 0.009 -0.059* 0.00001(0.022) (0.029) (0.004)

ct 0.114 -0.151 0.360 -0.017(0.168) (0.241) (0.227) (0.028)

pct 0.023 -0.042 0.904** 0.005(0.296) (0.383) (0.237) (0.034)

R2 (%) 20.870 22.318 41.925 15.787 24.877 22.956 44.361 25.551Adj. R2 (%) 15.450 16.997 37.977 10.062 19.405 17.343 40.336 20.165

Table 11: Estimates from pooled OLS regression with bank dummies, time trends and het-erogeneous AR parameters. Dependent variables: yit = ln(STDebtit), zit = ln(STAssetsit),(NI/TA)it = NetIncomeit/TotalAssetsit, (SRISK/TA)it = SRISKit/TotalAssetsit. Ro-bust standard errors in parentheses. * significant parameter at 5%; ** at 1%. Sample: 2107panel obs. over 2000Q1-2013Q1 (unbalanced), 44 banks. SRISK is the expected capitalshortfall of the bank in a crisis.

47

C.2 Short-term debt components

Dep. variable: yit FFRepo Br Dep Time Dep For Dep ComPaper OtherBor(SRISK/TA)it−1 -1.063** -1.217** 0.147 -0.363* -1.155* -2.330** -0.281

(0.245) (0.403) (0.518) (0.175) (0.531) (0.364) (0.377)

(NI/TA)it−1 2.354 0.152 -11.694 -1.660 10.880 17.540 3.249(2.278) (2.437) (8.376) (4.733) (6.282) (10.392) (9.375)

zit−1 -0.038 0.015 -0.028 -0.046* -0.191* -0.091 -0.233**(0.023) (0.051) (0.096) (0.019) (0.093) (0.083) (0.079)

# obs. 2107 1979 950 2096 1337 966 2035# banks 44 44 40 44 34 27 44R2 (%) 20.870 19.723 23.649 34.947 38.600 25.330 22.656

Adj. R2 (%) 15.450 13.843 12.279 30.459 33.355 18.187 17.152

Table 12: Estimates from pooled OLS regression with bank dummies, time trends and het-erogeneous AR parameters. Dependent variables: log of the different components of theshort term debt (see definitions in Appendix A): Fed funds and Repos (FFRepo), BrokeredDeposits (Br Dep), uninsured Time Deposits (Time Dep), Foreign Deposits (For Dep), Com-mercial Papers (ComPaper) and Other Borrowed Money (OtherBor). Robust standard errorsin parentheses. Robust standard errors in parentheses. * significant parameter at 5%; ** at1%. Sample: 2107 panel obs. over 2000Q1-2013Q1 (unbalanced), 44 banks. SRISK is theexpected capital shortfall of the bank in a crisis.

48

D Sample of banks

Name Ticker SNL ID RSSD ID Industry Market CapAmerican Express Company AXP 102700 1275216 Specialty Lender 60,834Bank of America Corporation BAC 100369 1073757 Bank 183,125The Bank of New York Mellon Corporation BK 100144 3587146 Bank 55,522BB&T Corporation BBT 100438 1074156 Bank 16,852Capital One Financial Corp. COF 103239 2277860 Bank 18,215Citigroup, Inc. C 4041896 1951350 Bank 146,644Fifth Third Bancorp FITB 100260 1070345 Bank 13,386The Goldman Sachs Group, Inc. GS 4039450 2380443 Broker Dealer 85,520JPMorgan Chase & Co. JPM 100201 1039502 Bank 146,622KeyCorp KEY 100334 1068025 Bank 9,117MetLife, Inc. MET 4051708 2945824 Insurance 45,636Morgan Stanley MS 103042 2162966 Broker Dealer 56,362The PNC Financial Services Group, Inc. PNC 100406 1069778 Bank 22,355Regions Financial Corporation RF 100233 3242838 Bank 16,439State Street Corporation STT 100447 1111435 Bank 31,360SunTrust Banks, Inc. STI 100449 1131787 Bank 21,756U.S. Bancorp USB 4047176 1119794 Bank 54,804Wells Fargo & Company WFC 100382 1120754 Bank 101,269Franklin Resources Inc. BEN 102719 1246216 Asset Manager 28,037Commerce Bancshares, Inc. CBSH 100184 2815235 Bank 3,229CIT Group Inc. CIT 102820 1036967 Specialty Lender NAComerica Incorporated CMA 100206 1029259 Bank 6,574Huntington Bancshares Incorporated HBAN 100307 1068191 Bank 5,401Marshall & Ilsley MI 100364 3594612 Bank 7,086M&T Bank Corporation MTB 100253 1037003 Bank 8,708National City Corp. NCC 100378 1069125 Bank 10,433Northern Trust Corporation NTRS 100386 1199611 Bank 16,843New York Community Bancorp Inc. NYCB 1024119 2132932 Savings/Thrift/Mutual 5,689The Charles Schwab Corporation SCHW 102775 1026632 Broker Dealer 29,547Synovus Financial Corporation SNV 100440 1078846 Bank 7,943UnionBanCal Corporation UB 1022285 1378434 Bank 6,776Wachovia Bank WB 100293 1073551 Bank 75,122Zions Bancorp. ZION 100501 1027004 Bank 4,995Associated Banc-Corp ASBC 100135 1199563 Bank 3,442Bank of Hawaii Corporation BOH 100161 1025309 Bank 2,506BOK Financial Corporation BOKF 100003 1883693 Bank 3,471Popular, Inc. BPOP 100165 2138466 Bank 2,971Cullen/Frost Bankers, Inc. CFR 100196 1102367 Bank 2,963

Table 13: Sample 1/2. Market capitalization in $m (Dec 30, 2007).

49

Name Ticker SNL ID RSSD ID Industry Market CapCity National Corporation CYN 100225 1131004 Bank 2,866Discover Financial Services DFS 4096334 3846375 Specialty Lender NAEast West Bancorp, Inc. EWBC 4040606 2734233 Bank 1,527First Citizens BancShares, Inc. FCNCA 100247 1105470 Bank 1,619First Horizon National Corporation FHN 100292 1094640 Bank 2,294Fulton Financial Corporation FULT 100294 1117129 Bank 1,946Hancock Holding Company HBHC 100308 1086533 Bank 1,207Prosperity Bancshares, Inc. PB 1018962 1109599 Bank 1,297SVB Financial Group SIVB 100433 1031449 Bank 1,673TCF Financial Corporation TCB 102002 2389941 Bank 2,272Webster Financial Corporation WBS 102030 1145476 Bank 1,710

Table 14: Sample 2/2. Market capitalization in $m (Dec 30, 2007).

50